Brightness temperature

Brightness temperature

Brightness temperature is the temperature at which a blackbody in thermal equilibrium with its surroundings would have to be in order to duplicate the observed intensity of an object at a frequency u.This is a useful concept only for radiation that obeys the Rayleigh–Jeans law, and it is extensively used in radio astronomy and planetary science.

For a blackbody, the Planck distribution gives:

::I( u) = frac{2 h u^{3{c^2}frac{1}{e^{frac{h u}{kT-1}

where

:*I( u)d u , is the amount of energy per unit surface per unit time per unit solid angle emitted in the frequency range between ν and ν+dν;:*T , is the temperature of the black body;:*h , is Planck's constant;:* u , is Frequency.:*c , is the speed of light; and:*k , is Boltzmann's constant.

In the Rayleigh-Jeans limit of low frequency, we find:

{I_{ u }=frac{2 u ^2k T}{c^2

This can be rewritten to define the brightness temperature as:

{T_b=frac{I_{ u } c^2}{2 u ^2 k

Brightness temperature is a useful diagnostic for temperature measurement if the astronomical source is a blackbody and we are in the Rayleigh-Jeans regime. It is not useful if the source is non-thermal and/or we are in the high frequency limit.

If the Planck distribution is reintroduced into the expression for brightness temperature we find:

{T_b=frac{h u}{k ( ext{Exp} [h u /k T] -1)

So, e.g. for the Sun, where the temperature may be estimated to be 6000K, we can plot the brightness temperature against wavelength and we find that when h u /k T is much less than one, the brightness temperature and physical temperature are the same, but at higher temperatures the brightness temperature is much lower.

ee also

Compare with color temperature and effective temperature.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • brightness temperature — skaistinė temperatūra statusas T sritis fizika atitikmenys: angl. brightness temperature vok. Leuchttemperatur, f rus. яркостная температура, f pranc. température de luminance, f; température radiométrique, f …   Fizikos terminų žodynas

  • brightness-temperature pyrometer — skaistinis pirometras statusas T sritis Standartizacija ir metrologija apibrėžtis Pirometras, lyginantis kūno, kurio temperatūra matuojama, ir pirometrinės lempos spinduliuojamąjį skaistį toje pačioje spektro srityje. atitikmenys: angl.… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • brightness-temperature pyrometer — skaistinis pirometras statusas T sritis fizika atitikmenys: angl. brightness temperature pyrometer vok. Helligkeitspyrometer, n; Leuchtdichtepyrometer, n rus. яркостный пирометр, m pranc. pyromètre à brillance, m …   Fizikos terminų žodynas

  • Temperature record — For extreme records instead of records as a set of data, see Temperature extremes For instrument derived temperature records, see Instrumental temperature record …   Wikipedia

  • température de luminance — skaistinė temperatūra statusas T sritis fizika atitikmenys: angl. brightness temperature vok. Leuchttemperatur, f rus. яркостная температура, f pranc. température de luminance, f; température radiométrique, f …   Fizikos terminų žodynas

  • température radiométrique — skaistinė temperatūra statusas T sritis fizika atitikmenys: angl. brightness temperature vok. Leuchttemperatur, f rus. яркостная температура, f pranc. température de luminance, f; température radiométrique, f …   Fizikos terminų žodynas

  • Color temperature — The CIE 1931 x,y chromaticity space, also showing the chromaticities of black body light sources of various temperatures (Planckian locus), and lines of constant correlated color temperature. Color temperature is a characteristic of visible light …   Wikipedia

  • Effective temperature — Star The effective temperature of a star is the temperature of a black body with the same luminosity per surface area (mathcal{F} {Bol}) as the star and is defined according to the Stefan–Boltzmann law mathcal{F} {Bol}=sigma T {eff}^4. Notice… …   Wikipedia

  • Geologic temperature record — The Geologic temperature record are changes in Earth s environment as determined from geologic evidence on multi million to billion (109) year time scales.Evidence for past temperaturesOur evidence for past temperatures comes mainly from isotopic …   Wikipedia

  • star — starless, adj. /stahr/, n., adj., v., starred, starring. n. 1. any of the heavenly bodies, except the moon, appearing as fixed luminous points in the sky at night. 2. Astron. any of the large, self luminous, heavenly bodies, as the sun, Polaris,… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”